Question 1

Evaluate the expression.Round your result to two decimal places.   $\arctan 2.6$

Accepted Answer

The arctangent of 2.6 is approximately 1.20 radians when rounded to two decimal places.

Question 2

Evaluate the expression.Round your result to two decimal places.   $\arccos 0.23$

Accepted Answer

The correct answer is found by calculating the arccos (also known as the inverse cosine) of 0.23. Using a calculator or a mathematical software that can compute inverse trigonometric functions, $\arccos(0.23)$ gives a value in radians. The value is approximately 1.34 radians when rounded to two decimal places.

Question 3

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.

Accepted Answer

To find the bearing, we calculate the angle using the tangent function, where tan(θ) = opposite/adjacent = 46/52. Solving for θ gives us the angle from the eastward direction, but bearings are measured clockwise from the north. Thus, we need to calculate 180° - θ to get the bearing from the north in a southward direction. The correct calculation leads to a bearing of approximately 131° 30'.

Question 4

Evaluate the expression.Round your result to two decimal places. $\arcsin 0.45$

Accepted Answer

The arcsine function, denoted as $\arcsin$, is the inverse of the sine function. It returns the angle whose sine is the given number. The value of $\arcsin 0.45$ is approximately 0.47 radians when rounded to two decimal places.

Question 5

Evaluate the expression.Round your result to two decimal places.   $\arcsin ( - 0.130 )$

Accepted Answer

The arcsin function gives the angle whose sine is the given number. For $\arcsin(-0.130)$, the result is approximately -0.130 radians, which rounds to -0.13.

Question 6

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

Accepted Answer

The answer of After leaving the runway, a plane's angle...

Question 7

Find the altitude of the isosceles triangle shown below if $\theta = 53 ^ { \circ }$ and $b = 25 \text { meters }$ .Round answer to two decimal places.

Accepted Answer

The answer of Find the altitude of the isosceles triangle...

Question 8

Evaluate the expression.Round your result to two decimal places.   $\arccos ( - 0.6 )$

Accepted Answer

The answer of Evaluate the expression.Round your result to two...

Question 9

Find the altitude of the isosceles triangle shown below if $\theta = 38 ^ { \circ }$ and $b = 8 \text { centimeters }$ .Round your answer to two decimal places.

Accepted Answer

The answer of Find the altitude of the isosceles triangle...

Question 10

Evaluate the expression.Round your result to two decimal places.   $\arctan 30$

Accepted Answer

The arctan (or inverse tangent) of 30 is approximately 1.54 radians.

Question 11

A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small aperture.Its height depends on the humidity and adhesion between granules.The angle of elevation of a pile, θ, is called the angle of repose.If the height of a pile of sand is 11 feet and its diameter is approximately 34 feet, determine the angle of repose.Round answer to nearest degree.

Accepted Answer

The answer of A granular substance such as sand naturally...

Question 12

A land developer wants to find the distance across a small lake in the middle of his proposed development.The bearing from A to B is $\mathrm { N } 31 ^ { \circ } \mathrm { W }$ .The developer leaves point A and travels 74 yards perpendicular to $\overline {A B}$ to point C.The bearing from C to point B is $\mathrm { N } 59 ^ { \circ } \mathrm { W }$ .Determine the distance, AB, across the small lake.Round distance to nearest yard.

Accepted Answer

The answer of A land developer wants to find the...

Question 13

Evaluate the expression.Round your result to two decimal places.   $\cos ^ { - 1 } 0.44$

Accepted Answer

The expression $\cos^{-1}(0.44)$ refers to the angle whose cosine is 0.44. Using a calculator, $\cos^{-1}(0.44) \approx 1.12$ radians.

Question 14

Evaluate the expression.Round your result to two decimal places.   $\arcsin \frac { 2 } { 3 }$

Accepted Answer

The arcsine function, denoted as $\arcsin$, is the inverse of the sine function. It returns the angle whose sine is the given number. The expression $\arcsin \frac { 2 } { 3 }$ asks for the angle whose sine is $\frac { 2 } { 3 }$. Using a calculator or a trigonometric table to find $\arcsin \frac { 2 } { 3 }$ gives a value of approximately 0.73 radians when rounded to two decimal places.

Question 15

If the sides of a rectangular solid are as shown, and $s = 4$ , determine the angle, $\theta$, between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

Accepted Answer

The answer of If the sides of a rectangular solid...

Question 16

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places.

Accepted Answer

We can use the trigonometric ratios to solve this problem. Let's first find the vertical component of the plane's velocity: Vertical component = 280 sin(17^o) = 280 sin(17.25) = 80.98 feet per second Now, we can use the kinematic equation: s = ut + 1/2 at^2 where s is the vertical displacement (11,000 feet), u is the initial velocity (80.98 feet per second), a is the acceleration due to gravity (-32.2 feet per second squared), and t is the time we're trying to find. Plugging in the values, we get: 11,000 = 80.98t - 16.1t^2 Rearranging and solving for t using the quadratic formula, we get: t = (80.98 ± √(80.98^2 + 4(16.1)(11,000))) / (2(-16.1)) t = (80.98 ± 629.83) / (-32.2) Since we're looking for the positive value of t: t = (80.98 + 629.83) / (-32.2) = 2.24 minutes (rounded to two decimal places) Therefore, the answer is C) 2.24 minutes.

Question 17

If $a = 12$ and $c = 18$ , determine the value of A.Round to two decimal places.

Accepted Answer

The answer of If $a = 12$ and \(c =...

Question 18

If $a = 11$ and $c = 28$ , determine the value of B.Round to two decimal places.

Accepted Answer

The answer of If $a = 11$ and \(c =...

Question 19

The angle of elevation of the sun is 26^o.Find the length, l, of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places.

Accepted Answer

The answer of The angle of elevation of the sun...

Question 20

Evaluate the expression.Round your result to two decimal places.   $\sin ^ { - 1 } 0.65$

Accepted Answer

The expression $\sin^{-1}(0.65)$ represents the angle whose sine is 0.65. Calculating this gives approximately 0.71 radians.

Quiz 4: Trigonometry

Evaluate the expression.Round your result to two decimal places. arctan⁡2.6\arctan 2.6arctan2.6

Evaluate the expression.Round your result to two decimal places. arccos⁡0.23\arccos 0.23arccos0.23

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.

Evaluate the expression.Round your result to two decimal places. arcsin⁡0.45\arcsin 0.45arcsin0.45

Evaluate the expression.Round your result to two decimal places. arcsin⁡(−0.130) \arcsin ( - 0.130 ) arcsin(−0.130)

After leaving the runway, a plane's angle of ascent is 17o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

Find the altitude of the isosceles triangle shown below if θ=53∘\theta = 53 ^ { \circ }θ=53∘ and b=25 meters b = 25 \text { meters }b=25 meters .Round answer to two decimal places.

Evaluate the expression.Round your result to two decimal places. arccos⁡(−0.6) \arccos ( - 0.6 ) arccos(−0.6)

Find the altitude of the isosceles triangle shown below if θ=38∘\theta = 38 ^ { \circ }θ=38∘ and b=8 centimeters b = 8 \text { centimeters }b=8 centimeters .Round your answer to two decimal places.

Evaluate the expression.Round your result to two decimal places. arctan⁡30\arctan 30arctan30

Evaluate the expression.Round your result to two decimal places. cos⁡−10.44\cos ^ { - 1 } 0.44cos−10.44

Evaluate the expression.Round your result to two decimal places. arcsin⁡23\arcsin \frac { 2 } { 3 }arcsin32​

If the sides of a rectangular solid are as shown, and s=4s = 4s=4 , determine the angle, θ\thetaθ , between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

After leaving the runway, a plane's angle of ascent is 17o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places. ​

If a=12a = 12a=12 and c=18c = 18c=18 , determine the value of A.Round to two decimal places.

If a=11a = 11a=11 and c=28c = 28c=28 , determine the value of B.Round to two decimal places.

The angle of elevation of the sun is 26o.Find the length, l, of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places.

Evaluate the expression.Round your result to two decimal places. sin⁡−10.65\sin ^ { - 1 } 0.65sin−10.65

Evaluate the expression.Round your result to two decimal places. $\arctan 2.6$

Evaluate the expression.Round your result to two decimal places. $\arccos 0.23$

Evaluate the expression.Round your result to two decimal places. $\arcsin 0.45$

Evaluate the expression.Round your result to two decimal places. $\arcsin ( - 0.130 )$

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

Evaluate the expression.Round your result to two decimal places. $\arccos ( - 0.6 )$

Evaluate the expression.Round your result to two decimal places. $\arctan 30$

Evaluate the expression.Round your result to two decimal places. $\cos ^ { - 1 } 0.44$

Evaluate the expression.Round your result to two decimal places. $\arcsin \frac { 2 } { 3 }$

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places.

If $a = 12$ and $c = 18$ , determine the value of A.Round to two decimal places.

If $a = 11$ and $c = 28$ , determine the value of B.Round to two decimal places.

The angle of elevation of the sun is 26^o.Find the length, l, of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places.

Evaluate the expression.Round your result to two decimal places. $\sin ^ { - 1 } 0.65$